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3 years ago

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Mathematics

1 answer:

OLga [1]3 years ago

3 0

Answer:

See below

Step-by-step explanation:

Here are some standard derivatives we will be using:

ƒ(x) ⟶ f'(x)

sin(x) ⟶ cos(x)

cos(x) ⟶ -sin(x)

$e^{ax} \longrightarrow ae^{ax}$

gh ⟶ gh' + hg'

$f(x) = e^{2x}\sin(x)\\f'(x) = e^{2x}\cos(x) + 2e^{2x}\sin(x) \\f''(x)=-e^{2x}\sin(x) + e^{2x}\cos(x)+2e^{2x}\cos(x) + 4e^{2x}\sin(x)$

$f''(x)= 4e^{2x}\cos(x)+ 3e^{2x}\sin(x)$

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What is the distance from point (– 1, 3) to the line 3x – 4y = 10?

natta225 [31]

Answer:

5 units

Step-by-step explanation:

The distance from a point (m, n ) to the line Ax + By + C = 0 is given by

d = $\frac{|Am+Bn+C|}{\sqrt{A^2+B^2} }$

For the point (- 1, 3 ) , with m = - 1 and n = 3

3x - 4y = 10 ( subtract 10 from both sides )

3x - 4y - 10 = 0

with A = 3 , B = - 4 , C = - 10

d = $\frac{|3(-1)+(-4)3-10|}{\sqrt{3^2+(-4)^2} }$

= $\frac{|-3-12-10|}{9+16}$

= $\frac{|-25|}{\sqrt{25} }$

= $\frac{25}{5}$

= 5

5 0

3 years ago

An aquifer holds 146,000 cubic feet of water. Water exits through a well at a steady rate of 500 cubic feet per day, and the aqu

m_a_m_a [10]

Answer:

The value of x = 100 ft^3/ day

Step-by-step explanation:

We need to look at what amount of water comes in and what amount of water leaves

What comes in: x ft^3/ day

What leaves : 500x ft^3/ day

We start with 146 000 ft^3

Water in tank = what we start with + what comes in - what leaves

water in tank = 146000 + x*d - 500*d where d is the number of days

After 365 days , the tank has 0 ft^3 of water

0 = 146000 + x*365 - 500*365

Multiply

0 = 146000 + 365x - 182500

Combine like terms

0 = -36500+365x

Add 36500 to each side

36500 = 36500-36500+365x

36500 = 365x

Divide by 365

36500/365 = 365x/365

100=x

The value of x = 100

8 0

3 years ago

Read 2 more answers

What is the prime factorization of 8

oksian1 [2.3K]

8
= 2^3
= 2* 2* 2

The prime factorization of 8 is 2* 2* 2.

Hope this helps~

5 0

3 years ago

Read 2 more answers

What is the slope passing through the points (6,5) and (5,3)

Rus_ich [418]

Answer:

$m=2$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Point (6, 5)

Point (5, 3)

Step 2: Find slope m

Substitute [SF]: $m=\frac{3-5}{5-6}$
Subtract: $m=\frac{-2}{-1}$
Divide: $m=2$

5 0

3 years ago

You have a jar containing 55 coins, consisting entirely of nickels and quarters, worth a

yawa3891 [41]

Answer: 22 quarters

Step-by-step explanation:

Let N be the number of nickels.

Then the number of quarters is (55-N)

The nickels contribute 5N cents to the total.

The quarters contribute 25*(55-N) cents to the total.

5N + 25*(55-N) = 715

5N + 1375 - 25N = 715

-20N = 715 - 1375 = -660

$N=\frac{-660}{-20}$

$=33$

$55-33=22$

So there is 22 quarters inside the jar.

Check to see if my answer is correct-

33*5 + 22*25 = 715 cents

6 0

3 years ago